Is my color management wrong?

To add to the comments below, Checking an Image on screen in ProPhoto RGB is not possible, but some large gamut print processes are larger than Adobe RGB in places, so ProPhoto has its place for those.  The normal workflow for printing to a high gamut device like described above is to export from Raw, which is just camera sensor data and contains no "gamut" into ProPhoto RGB, then convert to the printer profile in perceptual rendering so the gamut is not "Clipped" but this decision is image dependent.  The color space is huge, but the image may not inhabit all of that space.  That is why the space is used and why it is useful for this workflow.  

In a high-end workflow, stick to equipment choices that support it.  Adobe RGB is a large enough color space to provide bright colors, in good-quality print processes.  sRGB on the other hand is smaller than most high-quality print processes and only good for internet files.    

@Florblad  - @D Fosse writes: "ProPhoto is risky unless you're fully aware of the implications and understand how to handle such a huge color space. You will quickly end up with quite umanageable files that will not look good in any kind of output.

I'd recommend Adobe RGB for your master files, and sRGB for web and any other purpose where you don't know how it will be seen and treated."

He's right, ProPhoto is a massive colour space and users often push colours too far withing that colourspace. The fact that you cant see the entire ProPhotop gamut on any screen, let alone a P3 gamut screen is also an issue. Then the massive file has to be shrunk to a print gamut or maybe sTRGB for online use / sharing etc. Not ideal

You wrote:

"I take a picture in RAW on my Nikon and load it in my macbook (air M2) into Lightroom classic. I basically understand that Lightroom converts this RAW Information into something?"

Processing a RAW file creates an RGB file suitable for editing down the line.

It's good practice to archive the RAW too! It has more information than the RGB produced by processing it.

AND

"Is it nonsense to use AdobeRGB for my JPGs?

I want these JPGs for the archives and on my devices, for example my Macbook, to be able to fastly show them around to friends, family, ... and I want to do this with the best quality available. I hoped to get "more color details" with the AdobeRGB ones in comparison to the sRGB ones."

Using Adobe RGB for files to be shown on your Mac is fine. But for files which are to be shared and perhaps viewed outside of colour managed applicationsAdobe RGB may create issues. sRGB is better for web and sharing to non pro users IMO. So - you are right to make the sRGB version

You can read up about ICC profiles here

JPEGS - beware that format

I would not be resizing a JPEG but a TIFF then after resizing save as JPEG

Why?

A few notes on jpeg:

Jpeg files have compression applied, changing resolution or cropping and re-saving enhances the compression artefacts - this means that Jpeg is only really suitable for final file delivery/transfer - with the Jpeg created only once size and resolution (and any sharpening) have been completed. 

So,Jpeg is a far from ideal for editing and not OK for archiving or for any file that may need to be resaved, resized or cropped down the line.

Jpeg is the worst possible format if you want to keep high quality - you should always archive a copy of your original, ideally with any adjustment layers intact - if you work with layers.

Jpeg compression (at any setting*) really is "lossy”, irreversible and cumulative, so Jpegs should ONLY be used only for final delivery and only created from the original file format AFTER resizing & cropping to the FINAL size and crop.

To explain: any edits to size or crop, or even just re-saving a Jpeg file means further compression, potentially that’s very damaging.

The JPEG compression damage is not always immediately apparent, which is perhaps why it's still widely used - however, that compression will soon cause issues if you do further work and save again. That’s when you’ll see a Jpeg with some real issues.

*don’t imagine that selecting maximum quality for your Jpeg is preserving the original data, it’s still compressing a lot which discards information.

SO, don’t re-use Jpegs if any resizing or resaving is needed. Always go back to the PSD/ Tiff originals, Jpegs are essentially a 'use once and trash' file type.

@D Fosse wrote earlier:

jpeg is the worst possible format if you want to keep high quality. Jpeg compression is always destructive, non-reversible and cumulative. Not only is it discarding original data, but it's also introducing compression artifacts. Don't be fooled by the setting sometimes called "maximum quality" jpeg, meaning least compressed - there is no such thing as maximum quality when it comes to jpeg. It will degrade the image at any setting.

The only purpose of jpeg is to reduce file size for final delivery, with the implication that the immediately visible quality loss is acceptable. The reason jpeg still survives is because that size reduction is incredibly effective, it can shrink a file down to 2-5% of native size.

Never work on a jpeg, never resave a jpeg if you can avoid it. It will degrade further with every new save.

Printing is usually done from TIFF. PNG is a web format, not intended for print-related work.

Jpeg is usually fine provided you only save out once, at the very end, for final delivery. Save out a jpeg copy from the original master, which should be PSD or TIFF.

While the jpeg damage is normally not immediately apparent (which is why it's still widely used) - it will soon hit you if you do further work on it. Then a jpeg rapidly falls apart.

I hope this helps
neil barstow, colourmanagement net - adobe forum volunteer - co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management
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D Fosse is a world-class colour management expert so I hate to contradict him but as as you are a beginner I suggest IMO you stick to sRGB until you get your head around colour management workflows.

ProPhoto is risky unless you're fully aware of the implications and understand how to handle such a huge color space. You will quickly end up with quite umanageable files that will not look good in any kind of output.

I'd recommend Adobe RGB for your master files, and sRGB for web and any other purpose where you don't know how it will be seen and treated.

Side note:

DisplayP3 seems to be used everywhere in the Mac community nowadays, which is actually very unfortunate. It's basically a display profile - but if you use that on document level, you're actually disabling all color management, simply because the two profiles are the same (null transform). That's not how color management is supposed to work. The problem is that this encourages bad habits, and if the color management chain breaks, it will not be noticed. It will probably work within the Apple bubble, but cause problems outside it.

In short, avoid DisplayP3.

Is editing in ProPhotoRGB recommended with my Macbook set to Display P3?  - No, mainly because Display P3 is much smaller of a gamut than ProPhoto and your Macbook can not show you ProPhoto color space.  Use sRGB if that is your final intended color space for making pixels.  Adobe RGB is a good space to create images, but you need a wide gamut display to see it.  

sRGB is a very small gamut suitable for the internet, but for most printing purposes, it's too small.  Display P3 is an unknown quantity outside of your world.  But saving embedded images is always better than not.  

Color "details" will depend on your display.  As mentioned above, a wide gamut display benefits a photography workflow.